# Error analysis and how values in references are determined

Question 1:Most science textbooks have appendixes that have a value for some physical property of some object. This includes diameter of electrons, viscosity of fluids, boiling points, etc. My question is, are the values presented in such appendixes (or other data bases) averages?

Question 2: Also, suppose I try to calculate the boiling point of water using equations. I then compare my result with data obtained from the CRC Handbook. How would I determine how accurate my result is? Would I use percentages or is there another way to calculate the error? Note: by percentages I mean $$\vert\frac{result-reference\,\,value}{reference\,\,value}\vert\cdot100$$

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## 1 Answer

1) This varies by textbook. A common format you'll see is h=6.62606957(29)×10−34 (from Wikipedia: Planck constant). The digits in parentheses indicate they are uncertain. Hence, you'd expect that h is known to at least 0.00000001/6.6260957 (pretty well known.) Other references will explicitly state what the error bars are, or may simply cite the sources. You'd expect the error bars to be in the references in the latter case.

2) This is a fine way to determine your accuracy. I'm presuming, of course, that your error bars are much larger than the uncertainty in the boiling point of water. Don't be so sure that's the case! Water boiling point changes with air pressure, humidity, saline content...

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How would I determine uncertainty though? If the reference is an average, and if I know how many trials were conducted to determine the value of the reference, then I can use standard deviations. What method are you referring to and could you give me a reference? – Quantum MOCHACCINO Mar 11 '14 at 6:36
A really good book for this is An Introduction to Error Analysis by John R. Taylor. Chapter 3 is about how to combine uncertainties. You may not be able to use standard deviations alone. What if the experiment was done three times by three researchers, in such a way that all three researchers failed to account for a systematic error. You have to look at the actual experimental sources in this case. If a book doesn't report an error, sometimes that means the error bar is non-trivial! – ZSG Mar 11 '14 at 6:51